Maximum balloons from helium cylinder at constant temperature

[MadTay]

Homework Statement

A clown at a birthday party has brought along a helium cylinder, with which he intends to fill balloons. When full, each balloon contains 0.00260 m3 of helium at an absolute pressure of 1.10 x 10⁵ Pa. The cylinder contains helium at an absolute pressure of 1.80 x 10⁵ Pa and has a volume of 0.00310 m3. The temperature of the helium in the tank and in the balloons is the same and remains constant. What is the maximum number of people who will get a balloon?

Once I entered my first attempted answer, it gave me this as a hint: http://edugen.wileyplus.com/edugen/courses/crs7924/art/qb/qu/c14/EAT_12266037659380_3045928466969894.gif

Homework Equations

PV=nRT[/B]

The Attempt at a Solution

As stated above, since nRT does not change for either the cylinder or the balloons:

PVballoon/PVcylinder=number of balloons
(0.00260)(1.1x10⁵)/(0.00310)(1.8x10⁷)=195.1048951
So I entered 195 as the maximum number of people that would get a balloon, but it told me my answer was incorrect.

I worked another sample in the book with the exact same problem just different numbers, and I got the correct answer, so I am very lost.

 

[gneill]

After the last balloon is filled, will the cylinder be empty?

 

[Charles Link]

Please check your original numbers. The pressure in the tank and volume in the tank is such that it looks like it might fill about 2 balloons. The pressure in the tank needs to be much higher and/or its volume needs to be much larger to fill very many balloons. (I see you used a tank pressure of 1.8*E+7 rather than 1.8*E+5 in your calculation. You also have your fraction upside-down))

 

[MadTay]

I am so sorry, I made a mistake, the original number is supposed to be 1.8*E+7 not 1.8*E+5. I also typed my fractions upside down, but when I did the calculations my fractions were rightside up.

 

[Charles Link]

The 195 looks like the correct answer. Once the tank reaches a pressure of 1.1 E+5 Pa (after about 193 balloons), it will not be able to fill up any more balloons, but that is a very minor detail, and 195 is a good answer.